# Confusion about light exerting a force

1. Dec 29, 2012

### pigtwo

Hello everyone!

I've heard about things like solar sails, where the light from the sun would be used to push something to somewhere. I also heard something where someone calculated the weight that light from the sun has on an area the size of LA(it was something like 9 lbs). Seeing how light is massless, I don't see how this is possible.

I know the sun ejects actual non-massless(massful?) particles that I guess you could say accounts for this but I don't think this is what they are talking about.

The only thing I could think of that could cause this is that light has some amount of energy and given E = mc^2, we could replace all the mass terms with terms of energy. So we would take

$F = ma$
and turn it into
$F = \frac{E}{c^2} a$

Is this correct? For some reason it feels like I'm missing something.

Also, just so you know, I'm an engineering undergrad so I don't know a ton of physics. I've only taken Physics I and II. So mechanics and basic electromagnetics.

Another mini-semi related question:
I've also heard that something with more energy actually weighs more than the same thing with less energy. So a cup of water at 100 degrees would weigh more than the identical cup at 1 degree.

Which I guess makes sense because of E = mc^2. But I don't see why it would actually gain mass. To me E = mc^2 is just saying that energy and matter are two forms of the same thing essentially, but not that if one increases the other also increases.

So in this case I could see how if you somehow converted the thermal energy to mass, it would then clearly weigh more. But until then, it would weigh the same but have more thermal energy.

2. Dec 29, 2012

Staff Emeritus
Start with the fact that light carries momentum. That will get you where you are going.

3. Dec 29, 2012

### Bobbywhy

"I know the sun ejects actual non-massless(massful?) particles that I guess you could say accounts for this but I don't think this is what they are talking about."

True, the sun ocassionally emits gasses and particles called Coronal Mass Ejections. You are correct; these have nothing to do with "solar sails".

Cheers,
Bobbywhy

Last edited: Dec 29, 2012
4. Dec 30, 2012

### mrspeedybob

Right there you answered both of your own questions. Mass and energy are already the same thing. You don't have to convert one to the other. When you weigh something you are measuring its energy content.

Photons are said to be massless but that is not actually the case. What is meant by that is that they have no mass when at rest. However, they can never be at rest. Photons, by definition, travel at the speed of light so saying that the rest mass of a photon is pretty nonsensical.